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MULTIPLYING NUMBERS NEAR DIFFERENT BASESSQUARING NUMBERS NEAR A BASEA SUMMARY

LESSON 8 CHECKING AND DIVISIBILITY DIGIT SUM CHECK FOR DIVISION THE FIRST BY THE FIRST AND THE LAST BY THE LAST THE FIRST BY THE FIRST THE LAST BY THE LAST DIVISIBILITY BY 4 DIVISIBILITY BY 11 REMAINDER AFTER DIVISION BY 11 ANOTHER DIGIT SUM CHECK

LESSON 9 BAR NUMBERS REMOVING BAR NUMBERS ALL FROM 9 AND THE LAST FROM 10 SUBTRACTION CREATING BAR NUMBERS USING BAR NUMBERS

LESSON 10 SPECIAL MULTIPLICATION MULTIPLICATION BY 11 CARRIES LONGER NUMBERS BY ONE MORE THAN THE ONE BEFORE MULTIPLICATION BY NINES THE FIRST BY THE FIRST AND THE LAST BY THE LAST USING THE AVERAGE SPECIAL NUMBERS REPEATING NUMBERS PROPORTIONATELY DISGUISES

Description

This book is designed for teachers of children in grades 3 to 7. It shows how Vedic Mathematics can be used in a school course but does not cover all school topics (see contents). The book can be used for teachers who wish to learn the Vedic system or to teach courses on Vedic mathematics for this level.

The Manual contains many topics that are not in the other Manuals that are suitable for this age range and many topics that are also in Manual 2 are covered in greater detail here.

15 THE SOLUTION OF LINEAR AND NON-LINEAR DIFFERENTIAL, INTEGRAL AND INTEGRO-DIFFERENTIAL EQUATIONS

16 THE SOLUTION OF LINEAR AND NON-LINEAR PARTIAL DIFFERENTIAL EQUATIONS

Description

This is an advanced book of sixteen chapters on one Sutra ranging from elementary multiplication etc. to the solution of non-linear partial differential equations. It deals with (i) calculation of common functions and their series expansions, and (ii) the solution of equations, starting with simultaneous equations and moving on to algebraic, transcendental and differential equations. The text contains exercises and answers.

Book

Cover

Details

Contents

Introduction Preliminaries Provisions Definitions PROPOSITIONS Part A: Congruence, magnitudes and Lines Part B: Angles, parallels, triangles and quadrilaterals Part C: Concerning area equalities and similar triangles Part D: Elementary properties of a circle COMMENTARY Part I: Some basics Part II: Language and reason Part III: Comparisons with Euclid's Elements Part IV: Movement in geometry Part V: The valid use of figures Summary and Conclusions References APPENDICES Appendix 1: Application of the sixteen sutras to the present system of geometry Appendix 2: Alternative proofs and sequences in Part D Appendix 3: Further definitions

Description

This book demonstrates the kind of system that could have existed before literacy was widespread and takes us from first principles to theorems on elementary properties of circles. It presents direct, immediate and easily understood proofs. These are based on only one assumption (that magnitudes are unchanged by motion) and three additional provisions (a means of drawing figures, the language used and the ability to recognise valid reasoning). It includes discussion on the relevant philosophy of mathematics and is written both for mathematicians and for a wider audience.

Cover

Details

Contents

Chapter 8 is on Addition. Chapter 9 is on Subtraction and combined addition and subtraction.

Description

Following various lecture courses in London an interest arose for printed material containing the course material. This book of 12 chapters was the result covering a range topics from elementary arithmetic to cubic equations.

Contents

1. Addition - Completing the whole2. Addition from left to right3. Addition of list of numbers - Shudh method4. Subtraction - Base method5. Subtraction - Completing the whole6. Subtraction from left to right

1. Base Method2. Sub Base Method3. Vinculum4. Multiplication of complimentary numbers5. Multiplication by numbers consisting of all 9s6. Multiplication by 117. Multiplication by two-digit numbers from right to left8. Multiplication by three and four-digit numbers from right to left.

Chapter-5 Squaring and square Roots 53-57

Squaring

1. Squaring numbers ending in 52. Squaring Decimals and Fraction3. Squaring Numbers Near 504. Squaring numbers near a Base and Sub Base5. General method of Squaring - from left to right6. Number splitting to simplify Squaring Calculation7. Algebraic Squaring

3.1 Introduction to FCM and the Working of this Model 65 3.2 Definition and Illustration of Fuzzy Relational Maps (FRMS) 72 3.3 Definition of the New Fuzzy Dynamical System 77 43.4 Neutrosophic Cognitive Maps with Examples 78 3.5 Description of Neutrosophic Relational Maps 87 3.6 Description of the new Fuzzy Neutrosophic model 92

Chapter Four MATHEMATICAL ANALYSIS OF THE VIEWS ABOUT VEDIC MATHEMATICS USING FUZZY MODELS 95

4.1 Views of students about the use of Vedic Mathematics in their curriculum 97 4.2 Teachers views on Vedic Mathematics and its overall influence on the Students Community 101 4.3 Views of Parents about Vedic Mathematics 109 4.4 Views of Educationalists about Vedic Mathematics 114 4.5 Views of the Public about Vedic Mathematics 122

Chapter Five OBSERVATIONS 165

5.1 Students’ Views 165 5.2 Views of Teachers 169 5.3 Views of Parents 180 5.4 Views of the Educated 182 5.5 Observations from the Views of the Public 193

REFERENCE 197 INDEX 215 ABOUT THE AUTHORS 220

Description

The Vedas are considered divine in origin and are assumed to be revelations from God. In traditional Hinduism, the Vedas were to be learnt only by the upper caste Hindus. The lower castes (Sudras) and so-called untouchables (who were outside the Hindu social order) were forbidden from even hearing to its recitation. In recent years, there have been claims that the Vedas contain the cure to AIDS and the production of electricity. Here the authors probe into Vedic Mathematics (that gained renown during the revivalist Hindutva rule in India and was introduced into school syllabus in several states); and explore if it is really Vedic in origin or Mathematics in content. To gain a better understanding of its imposition, we interviewed students, teachers, parents, educationists and activists. We analyze this problem using models like Fuzzy Cognitive Maps (FCM), Fuzzy Relational Maps (FRM) and newly constructed Fuzzy Dynamical System (and their Neutrosophic Analogues). The issue of imposition of Vedic Mathematics into the school curriculum involves religious politics, caste supremacy, apart from elementary arithmetic so we use fuzzy and neutrosophic techniques to gain acute insight into how students have been affected because of this politically motivated syllabus revision.

Our Comments

We believe this paper was a reaction by some in the academic community to certain elements of the Hindu community trying to use Vedic Mathematics to promote Hinduism by teaching Vedic Mathematics in schools. It is our understanding that much of this initial teaching of Vedic Mathematics may have been implemented poorly by people who did not have a good grounding in their subject matter as they may have been more interested in promoting Hinduism than Vedic Mathematics, hence the academic reaction.

This paper was produced in 2006 and often appears in searches for Vedic Mathematics. The understanding and teaching of Vedic Mathematics has moved on a lot since this point in time.

Book

Hosted on the University of New Mexico (Gallup's branch campus) website